Adiabatic states derived from a spin-coupled diabatic transformation: semiclassical trajectory study of photodissociation of HBr and the construction of potential curves for LiBr+

The development of spin-coupled diabatic representations for theoretical semiclassical treatments of photodissociation dynamics is an important practical goal, and some of the assumptions required to carry this out may be validated by applications to simple systems. With this objective, we report here a study of the photodissociation dynamics of the prototypical HBr system using semiclassical trajectory methods. The valence (spin-free) potential energy curves and the permanent and transition dipole moments were computed using high-level ab initio methods and were transformed to a spin-coupled diabatic representation. The spin-orbit coupling used in the transformation was taken as that of atomic bromine at all internuclear distances. Adiabatic potential energy curves, nonadiabatic couplings and transition dipole moments were then obtained from the diabatic ones and were used in all the dynamics calculations. Nonadiabatic photodissociation probabilities were computed using three semiclassical trajectory methods, namely, coherent switching with decay of mixing (CSDM), fewest switches with time uncertainty (FSTU), and its recently developed variant with stochastic decoherence (FTSU/SD), each combined with semiclassical sampling of the initial vibrational state. The calculated branching fraction to the higher fine-structure level of the bromine atom is in good agreement with experiment and with more complete theoretical treatments. The present study, by comparing our new calculations to wave packet calculations with distance-dependent ab initio spin-orbit coupling, validates the semiclassical trajectory methods, the semiclassical initial state sample scheme, and the use of a distance-independent spin-orbit coupling for future applications to polyatomic photodissociation. Finally, using LiBr(+) as a model system, it is shown that accurate spin-coupled potential curves can also be constructed for odd-electron systems using the same strategy as for HBr.     

Theoretical investigation of the dissociation dynamics of vibrationally excited vinyl bromide on an ab initio potential-energy surface obtained using modified novelty sampling and feedforward neural networks. II. Numerical application of the method

A previously reported method for conducting molecular dynamics simulations of gas-phase chemical dynamics on ab initio potential-energy surfaces using modified novelty sampling and feedforward neural networks is applied to the investigation of the unimolecular dissociation of vinyl bromide. The neural network is fitted to a database comprising the MP4(SDQ) energies computed for 71 969 nuclear configurations using an extended basis set. Dissociation rate coefficients and branching ratios at an internal excitation energy of 6.44 eV for all six open reaction channels are reported. The distribution of vibrational energy in HBr formed in three-center dissociation is computed and found to be in excellent accord with experimental measurements. Computational requirements for the electronic structure calculations, neural network training, and trajectory calculations are given. The weight and bias matrices required for implementation of the neural network potential are made available through the Supplementary Material.     

Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy

The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence of excited-state asymmetric vibrations in those experiments.     

Normal Auger spectra of Br in alkali bromide molecules

Molecular Auger electron spectra following the bromine 3d ionization in gas-phase alkali bromides and in HBr were studied both experimentally and theoretically. The AES for HBr and CsBr were measured using photoexcitation, and for LiBr, NaBr, and KBr by using electron impact. These results are compared with the theoretical spectra from nonrelativistic ab initio calculations and one-center approximation and with the spectra of Br(-), computed with the multiconfiguration Dirac-Fock method.     

Compartmental modeling of the fluorescence anisotropy decay of a cylindrically symmetric brownian rotor: Identifiability analysis.

We present the results of the deterministic identifiability analysis based on similarity transformation for models of one-state excited-state events of cylindrically symmetric rotors in isotropic environments undergoing rotational diffusion described by Brownian reorientation. Such an analysis on error-free time-resolved fluorescence (anisotropy) data can reveal whether the parameters of the considered model can be determined. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to construct, in convenient matrix form, expressions of the sum S(t) = I(parallel)(t) + 2I(perpendicular)(t), the difference D(t) = I(parallel)(t) - I(perpendicular)(t), and the time-resolved fluorescence anisotropy r(t) = D(t)/S(t). The identifiability analysis of r(t) demonstrates that the rotational diffusion coefficients D(parallel) and D(perpendicular) for rotation respectively about and perpendicular to the symmetry axis can be uniquely resolved. However, the polar and azimuthal angles defining the absorption and emission transition moments in the molecular reference frame are not individually identifiable. Nevertheless, the difference between the polar angles of these transition moments is uniquely determined.     

Excited-state dynamics of donor-acceptor bridged systems containing a boron-dipyrromethene chromophore: interplay between charge separation and reorientational motion

The excited-state dynamics of a series of electron donor-acceptor bridged systems (DABS) consisting of a boron-dipyrromethene chromophore covalently linked to a dinitro-substituted triptycene has been investigated using femtosecond time-resolved spectroscopy. The chromophores differ by the number of bromine atom substituents. The fluorescence lifetime of the DABS without any bromine atom is strongly reduced when going from toluene to polar solvents, this shortening being already present in chloroform. This effect is about 10 times weaker with a single bromine atom and negligible with two bromine atoms on the chromophore. The excited-state lifetime shortening is ascribed to a charge transfer from the excited chromophore to a nitrobenzene moiety, the driving force of this process depending on the number of bromine substituents. The occurrence of this process is further confirmed by the investigation of the excited-state dynamics of the chromophore alone in pure nitrobenzene. Surprisingly, no correlation between the charge separation time constant and the dielectric properties of the solvents could be observed. However, a good correlation between the charge separation time constant and the diffusional reorientation time of the chromophore alone, measured by fluorescence anisotropy, was found. Quantum chemistry calculations suggest that quasi-free rotation about the single bond linking the chromophore to the triptycene moiety permits a sufficient coupling of the donor and the acceptor to ensure efficient charge separation. The charge separation dynamics in these molecules is thus controlled by the reorientational motion of the donor relative to the acceptor.     

Compartmental modeling of reversible intermolecular two-state excited-state processes coupled with rotational diffusion or with added quencher

Analysis of related time-resolved fluorescence measurements can possibly lead to the determination of the kinetic parameters of excited-state processes. A deterministic identifiability analysis on an error-free fluorescence decay data surface has to be executed to verify whether the parameters of a particular model can be determined and may point to the minimal experimental conditions under which this will become possible. In this work, similarity transformation is chosen as an identifiability analysis approach because it also gives the explicit relationships between the true and alternative model parameters. Results are presented for two kinetic models of a reversible intermolecular two-state excited-state process in isotropic environments: (a) with coupled species-dependent rotational diffusion described by Brownian reorientation and (b) with added quencher. For model a, both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation in the latter, are considered. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to define the sum S(t) = I( parallel)(t) + 2 I( perpendicular)(t) and the difference D(t) = I(parallel)(t) - I(perpendicular)(t) function. The identifiability analysis is carried out using the S(t) and D(t) functions. The analysis involving S(t) shows that two physically acceptable possible solutions for the overall rate constants of the excited-state process exist. Inclusion of information from polarized fluorescence measurements on the rotational kinetic behavior contained in D(t) results in the unique set of rate constants and rotational diffusion coefficients when the rotational diffusion coefficients are different. For model b, it is shown that addition of quencher plays formally the same role as rotational diffusion as far as the identification is concerned. When the quenching rate constants are different, the rate constants of a reversible intermolecular two-state excited-state process with added quencher can be uniquely determined.     

Identifiability analysis of models for reversible intermolecular two-state excited-state processes coupled with species-dependent rotational diffusion monitored by time-resolved fluorescence depolarization

A deterministic identifiability analysis of the kinetic model for a reversible intermolecular two-state excited-state process with species-dependent rotational diffusion described by Brownian reorientation is presented. The cases of both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation on interconversion in the latter case, are specifically considered. The identifiability analysis is carried out in terms of compartmental modeling based on the S(t) identical with I( parallel)(t)+2I( perpendicular)(t) and D(t) identical with I( parallel)(t)-I( perpendicular)(t) functions, where I( parallel)(t) and I( perpendicular)(t) are the delta-response functions for fluorescence, polarized, respectively, parallel and perpendicular to the electric vector of linearly polarized excitation. It is shown that, from polarized time-resolved fluorescence data collected at two concentrations of coreactant and three appropriately chosen emission wavelengths, (a) a unique set of rate constants for the overall excited-state process is always obtained by making use of polarized measurements and (b) the rotational diffusion constants and geometrical factors associated with the different anisotropy decay components can be uniquely determined and assigned to each species. The geometrical factors are determined by the absorption and emission transitions in the two rotating species. For spherical rotors, these factors depend directly on the relative orientations of the transition moments, while for cylindrically symmetric rotors they depend on the orientations with respect to each other and to the symmetry axis.     

Preliminary communication Photopyroelectric investigation of the thermal conductivity anisotropy in oriented liquid crystals

Photopyroelectric measurements of heat transport parallel or perpendicular to the director have been carried out for compounds of the 4,4-dialkylazoxybenzene homologous series. A theoretical expression based on molecular length-width ratios predicts a thermal conductivity anisotropy ratio which is between 1.5 and 2 times larger than experimentally observed. However, the predicted order parameter temperature dependence seems to be consistent with the experimental data.     

Molecular dynamics study of anisotropic translational and rotational diffusion in liquid benzene

Equilibrium NPT and NVT molecular dynamics simulations were performed on liquid benzene over an extended range of temperature (from 260 to 360 K) using the COMPASS force field. Densities and enthalpies of vaporization (from cohesive energy densities) were within 1% of experiment at all temperatures. tumbling and spinning rotational diffusion coefficients, D(perpendicular) and D(parallel), computed as a function of temperature, agreed qualitatively with the results of earlier reported experimental and computational investigations. Generally, it was found that D(parallel)/D(perpendicular) approximately 1.4-2.5 and the activation energy for tumbling was significantly greater than for spinning about the C6 axis [Ea(D(perpendicular)) = 8.1 kJ mol(-1) and Ea(D(parallel)) = 4.5 kJ mol(-1)]. Calculated translational diffusion coefficients were found to be in quantitative agreement with experimental values at all temperatures [deviations were less than the scatter between different reported measurements]. In addition, translational diffusion coefficients were computed in the molecule-fixed frame to yield values for Dxy (diffusion in the plane of the molecule) and Dz (diffusion perpendicular to the plane). It was found that the ratio Dxy/Dz approximately 2.0, and that the two coefficients have roughly equal activation energies. This represents the first atomistic molecular dynamics study of translational diffusion in the molecular frame.     

Photodissociation of HI and DI: polarization of atomic photofragments

The complete angular momentum distributions and vector correlation coefficients (orientation and alignment) of ground state I((2)P(32)) and excited state I((2)P(12)) atoms resulting from the photodissociation of HI have been computed as a function of photolysis energy. The orientation and alignment parameters a(Q) ((K))(p) that describe the coherent and incoherent contributions to the angular momentum distributions from the multiple electronic states accessed by parallel and perpendicular transitions are determined using a time-dependent wave packet treatment of the dissociation dynamics. The dynamics are based on potential energy curves and transition dipole moments that have been reported previously [R. J. LeRoy, G. T. Kraemer, and S. Manzhos, J. Chem. Phys. 117, 9353 (2002)] and used to successfully model the scalar (total cross section and branching fraction) and lowest order vector (anisotropy parameter beta) properties of the photodissociation. Predictions of the a(Q) ((K))(p), parameters for the isotopically substituted species DI are reported and contrasted to the analogous HI results. The resulting polarization for the corresponding H/D partners are also determined and demonstrate that both H and D atoms produced can be highly spin polarized. Comparison of these predictions for HI and DI with experimental measurement will provide the most stringent test of the current model for the electronic structure and the interpretation of the dissociation based on noncoupled excited state dynamics.     

Monte Carlo determination of the oscillator strength and excited state lifetime for the Li 22S → 22P transition

A recently developed Monte Carlo method is used to compute the 2²S → 2²P transition dipole moment of Li. This approach employs a guided Metropolis random walk with quantum Monte Carlo “side” walks to sample the required probability distributions. The transition dipole moment is employed to obtain the oscillator strength and excited-state lifetime. Our most accurately converged calculations yield an oscillator strength of 0.742(7) and excited-state lifetime of 27.41(35) ns. These results are in excellent agreement with precise experimental measurements of 0.742(1) and 27.29(4) ns, respectively. In addition, single-state expectation values are computed for both states. Monte Carlo parameters, such as the time step size and the convergence time, are varied in order to study their effect on computed results.     

Identifiability of models for intramolecular two-state excited-state processes with added quencher and coupled species-dependent rotational diffusion

The parameters describing the kinetics of excited-state processes can possibly be recovered by analysis of the fluorescence decay surface measured as a function of the experimental variables. The identifiability analysis of a photophysical model assuming errorless time-resolved fluorescence data can verify whether the model parameters can be determined and may lead to the minimal experimental conditions under which this is possible. In this work, we used the method of similarity transformation to investigate the identifiability of three kinetic models utilized to describe the time-resolved fluorescence of reversible intramolecular two-state excited-state processes in isotropic environments: (1) model without added quencher, (2) model with added quencher, (3) model with added quencher coupled with species-dependent rotational diffusion described by Brownian reorientation. Without a priori information, model 1 is not identifiable. For model 2, two sets of quenching rate constants and combinations of excited-state deactivation/exchange rate constants are possible, but they cannot be allocated to a specific excited-state species. For both sets, upper and lower limits on the excited-state deactivation/exchange rate constants can be obtained. For model 3, both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation in the latter, are considered. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized parallel and perpendicular, respectively, to the electric vector of linearly polarized excitation, are used to define the sum S(t) identically equal to I(parallel)(t) + 2 I(perpendicular)(t) and the difference D(t) identically equal to I(parallel)(t) - I(perpendicular)(t). The identifiability analysis is performed using the S(t) and D(t) functions. Also for model 3, two sets of kinetic parameters (i.e., quenching rate constants, combinations of deactivation/exchange rate constants, and rotational diffusion coefficients) exist, but these parameters cannot be assigned unequivocally to a specific species. For the three models, an infinite number of alternative spectroscopic parameters associated with excitation and emission are found.     

Rotational structure of small 4He clusters seeded with HF, HCl, and HBr molecules

Diffusion Monte Carlo calculations are performed for ground and excited rotational states of HX(4He)N, complexes with N相似文献   

Theoretical study of the benzene excimer using time-dependent density functional theory

A theoretical characterization of the potential energy surfaces of the singlet benzene excimer states derived from the B2u monomer excited state has been performed using time-dependent density functional theory. The excited-state potential energy surfaces were initially characterized by computations along the parallel and perpendicular intermolecular translational coordinates. These calculations predict that the lowest excited state for parallel translation is bound with a minimum at 3.15 angstroms and with a binding energy of 0.46 eV, while the perpendicular translational coordinate was essentially found to be a repulsive state. At the calculated minimum distance, the effect of in-plane rotation, out-of-plane rotation, and slipped-parallel translation were examined. The rotational calculations predict that deviations from the D6h geometry lead to a destabilization of the excimer state; however, small angular variations in the range of 0 degrees -10 degrees are predicted to be energetically feasible. The slipped-parallel translational calculations also predict a destabilizing effect on the excimer state and were found to possess barriers to this type of dissociation in the range of 0.50-0.61 eV. When compared to experimentally determined values for the benzene excimer energetics, the calculated values were found to be in semiquantitative agreement. Overall, this study suggests that the time-dependent density functional theory method can be used to characterize the potential energy surfaces and the energetics of aromatic excimers with reasonable accuracy.     

State-to-state quantum dynamics of the H + HBr reaction: competition between the abstraction and exchange reactions

Quantum state-to-state dynamics for the H + HBr(υ(i) = 0, j(i) =0) reaction was studied on an accurate ab intio potential energy surface for the electronic ground state of BrH(2). Both the H + HBr → H(2) + Br abstraction reaction and the H' + HBr → H'Br + H exchange reaction were investigated up to a collision energy of 2.0 eV. It was found that the abstraction channel is dominant at lower collision energies, while the exchange channel becomes dominant at higher collision energies. The total integral cross section of the abstraction reaction at a collision energy of 1.6 eV was found to be 1.37 A?(2), which is larger than a recent quantum mechanical result (1.06 A?(2)) and still significantly smaller than the experimental value (3 ± 1 A?(2)). Meanwhile, similar to the previous theoretical study, our calculations also predicted much hotter product rotational state distributions than those from the experimental study. This suggests that further experimental investigations are highly desirable to elucidate the dynamic properties of the title reactions.     

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order M?ller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.     

The photodissociation dynamics of O2 at 193 nm: an O3PJ angular momentum polarization study

In the following paper we present translational anisotropy and angular momentum polarization data for O((3)P(1)) and O((3)P(2)) products of the photodissociation of molecular oxygen at 193 nm. The data were obtained using polarized laser photodissociation coupled with resonantly enhanced multiphoton ionization and velocity-map ion imaging. Under the jet-cooled conditions employed, absorption is believed to be dominated by excitation into the Herzberg continuum. The experimental data are compared with previous experiments and theoretical calculations at this and other wavelengths. Semi-classical calculations performed by Groenenboom and van Vroonhoven [J. Chem. Phys, 2002, 116, 1965] are used to estimate the alignment parameters arising from incoherent excitation and dissociation and these are shown to agree qualitatively well with the available experimental data. Following the work of Alexander et al. [J. Chem. Phys, 2003, 118, 10566], orientation and alignment parameters arising from coherent excitation and dissociation are modelled more approximately by estimating phase differences generated subsequent to dissociation via competing adiabatic pathways leading to the same asymptotic products. These calculations lend support to the view that large values of the coherent alignment moments, but small values of the corresponding orientation moments, could arise from coherent excitation of (and subsequent dissociation via) parallel and perpendicular components of the Herzberg I, II and III transitions.     

Photodissociation of HI and DI: testing models for electronic structure via polarization of atomic photofragments

The photodissociation dynamics of HI and DI are examined using time-dependent wave-packet techniques. The orientation and alignment parameters aQ(K) (p) are determined as a function of photolysis energy for the resulting ground-state I(2P(3/2)) and excited-state I(2P(1/2)) atoms. The aQ(K) (p) parameters describe the coherent and incoherent contributions to the angular momentum distributions from the A 1pi(1), a 3pi(1), and t 3sigma(1) electronic states accessed by perpendicular excitation and the a 3pi(0+) state accessed by a parallel transition. The outcomes of the dynamics based on both shifted ab initio results and three empirical models for the potential-energy curves and transition dipole moments are compared and contrasted. It is demonstrated that experimental measurement of the aQ(K) (p) parameters for the excitation from the vibrational ground state (upsilon=0) would be able to distinguish between the available models for the HI potential-energy curves and transition dipole moments. The differences between the aQ(K) (p) parameters for the excitation from upsilon=0 stand in sharp contrast to the scalar properties, i.e., total cross section and I* branching fraction, which require experimental measurement of photodissociation from excited vibrational states (upsilon>0) to distinguish between the models.     

Exciton migration in rigid-rod conjugated polymers: an improved Förster model

The dynamics of interchain and intrachain excitation energy transfer taking place in a polyindenofluorene endcapped with perylene derivatives is explored by means of ultrafast spectroscopy combined with correlated quantum-chemical calculations. The experimental data indicate faster exciton migration in films with respect to solution as a result of the emergence of efficient channels involving hopping between chains in close contact. These findings are supported by theoretical simulations based on an improved Forster model. Within this model, the rates are expressed according to the Fermi golden rule on the basis of (i) electronic couplings that take account of the detailed shape of the excited-state wave functions (through the use of a multicentric monopole expansion) and (ii) spectral overlap factors computed from the simulated acceptor absorption and donor emission spectra with explicit coupling to vibrations (considered within a displaced harmonic oscillator model); inhomogeneity is taken into account by assuming a distribution of chromophores with different conjugation lengths. The calculations predict faster intermolecular energy transfer as a result of larger electronic matrix elements and suggest a two-step mechanism for intrachain energy transfer with exciton hopping along the polymer backbone as the limiting step. Injecting the calculated hopping rates into a set of master equations allows the modeling of the dynamics of exciton transport along the polyindenofluorene chains and yields ensemble-averaged energy-transfer rates in good agreement with experiment.